Goodness-of-fit Test for the Stochastic Volatility Model Based on the Noisy Observations

Abstract

In financial economics, the continuous-time stochastic processes have important applications. A goodness-of-fit test for stationary distributions of continuous time stochastic processes plays an important role in building up stochastic differential equation models. Furthermore, for the high frequency financial data, the efficient price is commonly assumed to follow a continuous time stochastic volatility model, contaminated with a microstructure noise. Manifestly, the current issue is much more challenging since the volatility process is latent and the price process is contaminated with noise. In this study, we consider a goodness-of-fit test problem for the efficient price models based on discretely noisy observed samples and employ the empirical characteristic function based goodness-of-fit test. Simultaneously, we investigate the empirical distribution of the microstructure noise from a real data analysis. It is shown that the proposed test asymptotically follows a weighted sum of products of centered normal random variables. To evaluate the proposed test, a simulation study to use a bootstrap method is implemented. A real data analysis is provided for illustration. Keywords: Bootstrap; empirical characteristic function; goodness-of-fit; stochastic volatility models; V-statistics.?